{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy as np\n",
    "\n",
    "# array1 = np.array([1, 2, 3])\n",
    "# array2 = np.array([4, 5, 6])\n",
    "# result = array1 * array2\n",
    "# print(array1.max())\n",
    "# print(array2.min())\n",
    "# print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(m,n)左边闭合，右开"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for i in range(0, 10):\n",
    "#     print(i - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "学号：2022302141211\n",
      "姓名：刘维康\n",
      "标准向前列递推法\n",
      "-----------------------\n",
      "L      M     P_l_m\n",
      "0      0     1.0000000000000000\n",
      "\n",
      "1      0     1.5000000000000000\n",
      "1      1     0.8660254037844385\n",
      "\n",
      "2      0     1.3975424859373686\n",
      "2      1     1.6770509831248421\n",
      "2      2     0.4841229182759270\n",
      "\n",
      "3      0     0.8592329428042205\n",
      "3      1     2.2277546150777026\n",
      "3      2     1.1092649593311779\n",
      "3      3     0.2614562582918985\n",
      "\n",
      "4      0     0.0703125000000011\n",
      "4      1     2.3107045394749210\n",
      "4      2     1.7818666695701451\n",
      "4      3     0.6792832849776297\n",
      "4      4     0.1386581199163971\n",
      "\n",
      "5      0     -0.7405100286552910\n",
      "5      1     1.8565375211351971\n",
      "5      2     2.2993847894939754\n",
      "5      3     1.2465314425264331\n",
      "5      4     0.3982651281554629\n",
      "5      5     0.0727129315194776\n",
      "\n",
      "6      0     -1.3485606821315490\n",
      "6      1     0.9502128764114142\n",
      "6      2     2.4747031178290517\n",
      "6      3     1.8559287053259697\n",
      "6      4     0.8104756887038498\n",
      "6      5     0.2270460558984087\n",
      "6      6     0.0378410093164014\n",
      "\n",
      "7      0     -1.5886127476866170\n",
      "7      1     -0.1926306662546085\n",
      "7      2     2.1970568748495238\n",
      "7      3     2.3528549723313663\n",
      "7      4     1.3441448075246873\n",
      "7      5     0.5029904227018065\n",
      "7      6     0.1269226037530147\n",
      "7      7     0.0195845829450013\n",
      "\n",
      "8      0     -1.3968077255243423\n",
      "8      1     -1.2840971771537601\n",
      "8      2     1.4717387242616695\n",
      "8      3     2.5775398544029358\n",
      "8      4     1.9145600012956345\n",
      "8      5     0.9101775580273601\n",
      "8      6     0.3022261383420487\n",
      "8      7     0.0699309487022940\n",
      "8      8     0.0100936630144888\n",
      "\n",
      "9      0     -0.8263391480132622\n",
      "9      1     -2.0421330741664407\n",
      "9      2     0.4277175808575171\n",
      "9      3     2.4135139392399858\n",
      "9      4     2.3961106448468756\n",
      "9      5     1.4206373776183709\n",
      "9      6     0.5885464520738094\n",
      "9      7     0.1773184823555708\n",
      "9      8     0.0381027423024033\n",
      "9      9     0.0051851264689804\n",
      "\n",
      "10     0     -0.0322527014053118\n",
      "10     1     -2.2674987894834158\n",
      "10     2     -0.7098003241787529\n",
      "10     3     1.8284787603168744\n",
      "10     4     2.6507089761734521\n",
      "10     5     1.9635936240588954\n",
      "10     6     0.9909812643431387\n",
      "10     7     0.3679560714038176\n",
      "10     8     0.1021464026905574\n",
      "10     9     0.0205778327300110\n",
      "10     10    0.0026565867821458\n",
      "\n",
      "11     0     0.7707132679207773\n",
      "11     1     -1.8988880661969372\n",
      "11     2     -1.6752290192993409\n",
      "11     3     0.8948198565214773\n",
      "11     4     2.5654995808925962\n",
      "11     5     2.4328008884605223\n",
      "11     6     1.4838996572464538\n",
      "11     7     0.6611469414554979\n",
      "11     8     0.2241911468199977\n",
      "11     9     0.0579942980595017\n",
      "11     10    0.0110336335792426\n",
      "11     11    0.0013581464081886\n",
      "\n",
      "12     0     1.3660132884979226\n",
      "12     1     -1.0312183624279738\n",
      "12     2     -2.2321981539196400\n",
      "12     3     -0.2178444823439283\n",
      "12     4     2.0895688450015983\n",
      "12     5     2.7069378723292417\n",
      "12     6     2.0059905827933333\n",
      "12     7     1.0591314199711055\n",
      "12     8     0.4264453612633062\n",
      "12     9     0.1338424501531922\n",
      "12     10    0.0325402615148122\n",
      "12     11    0.0058809464577496\n",
      "12     12    0.0006930761866783\n",
      "\n",
      "13     0     1.5934413671493517\n",
      "13     1     0.1080457385914444\n",
      "13     2     -2.2380537764087309\n",
      "13     3     -1.2780520990472262\n",
      "13     4     1.2585306074580855\n",
      "13     5     2.6793432668546018\n",
      "13     6     2.4648820790509296\n",
      "13     7     1.5380497143611487\n",
      "13     8     0.7243532821675824\n",
      "13     9     0.2678564142076961\n",
      "13     10    0.0785948395693181\n",
      "13     11    0.0180803240590107\n",
      "13     12    0.0031188428400523\n",
      "13     13    0.0003531394120898\n",
      "\n",
      "14     0     1.3920080206964278\n",
      "14     1     1.2184012650199851\n",
      "14     2     -1.6853878686432444\n",
      "14     3     -2.0478215884219297\n",
      "14     4     0.1983169938796054\n",
      "14     5     2.2898471557833604\n",
      "14     6     2.7524286242201041\n",
      "14     7     2.0434879667600052\n",
      "14     8     1.1181919646022589\n",
      "14     9     0.4791915359779776\n",
      "14     10    0.1646757291920562\n",
      "14     11    0.0455254322268159\n",
      "14     12    0.0099634337688264\n",
      "14     13    0.0016469325775730\n",
      "14     14    0.0001796950762195\n",
      "\n",
      "15     0     0.8161162745775881\n",
      "15     1     2.0058439278790616\n",
      "15     2     -0.7086010476614186\n",
      "15     3     -2.3438483249050810\n",
      "15     4     -0.8952828510077406\n",
      "15     5     1.5497111187161341\n",
      "15     6     2.7686102776666877\n",
      "15     7     2.4935270940359411\n",
      "15     8     1.5855184614179201\n",
      "15     9     0.7804146028773391\n",
      "15     10    0.3086562289882352\n",
      "15     11    0.0994651844188702\n",
      "15     12    0.0260683360445496\n",
      "15     13    0.0054519407087358\n",
      "15     14    0.0008664582792652\n",
      "15     15    0.0000913327219996\n",
      "\n",
      "16     0     0.0207627034508979\n",
      "16     1     2.2611748965367129\n",
      "16     2     0.4472260764377938\n",
      "16     3     -2.0881331950191138\n",
      "16     4     -1.7981658609242837\n",
      "16     5     0.5514513636121325\n",
      "16     6     2.4489303656886179\n",
      "16     7     2.7905965323844808\n",
      "16     8     2.0772014461934587\n",
      "16     9     1.1703939224069360\n",
      "16     10    0.5272659622498395\n",
      "16     11    0.1944976917395164\n",
      "16     12    0.0591910016095081\n",
      "16     13    0.0147809782158498\n",
      "16     14    0.0029651559340839\n",
      "16     15    0.0004543745549318\n",
      "16     16    0.0000463744088203\n",
      "\n",
      "17     0     -0.7802153212018185\n",
      "17     1     1.9160591637274935\n",
      "17     2     1.4876970686856514\n",
      "17     3     -1.3337117664358633\n",
      "17     4     -2.3111523801943221\n",
      "17     5     -0.5413981632804866\n",
      "17     6     1.7882019519515295\n",
      "17     7     2.8410415562681317\n",
      "17     8     2.5194975344621655\n",
      "17     9     1.6278654184634567\n",
      "17     10    0.8308478521494460\n",
      "17     11    0.3469125710500147\n",
      "17     12    0.1203309650962739\n",
      "17     13    0.0347805649960086\n",
      "17     14    0.0083100700902641\n",
      "17     15    0.0016041096457797\n",
      "17     16    0.0002375981419910\n",
      "17     17    0.0000235257216508\n",
      "\n",
      "18     0     -1.3716147880517904\n",
      "18     1     1.0617059137203992\n",
      "18     2     2.1449128455982032\n",
      "18     3     -0.2573060410049908\n",
      "18     4     -2.3115232276854103\n",
      "18     5     -1.5244461992224219\n",
      "18     6     0.8534322246115651\n",
      "18     7     2.5787548529853730\n",
      "18     8     2.8234931696505314\n",
      "18     9     2.1078942122196782\n",
      "18     10    1.2172289603598268\n",
      "18     11    0.5714629822449151\n",
      "18     12    0.2232627813311921\n",
      "18     13    0.0732923337517380\n",
      "18     14    0.0202147662187822\n",
      "18     15    0.0046375350790911\n",
      "18     16    0.0008637462490957\n",
      "18     17    0.0001239294287995\n",
      "18     18    0.0000119251148463\n",
      "\n",
      "19     0     -1.5946375500435064\n",
      "19     1     -0.0749879086419554\n",
      "19     2     2.2477552984399178\n",
      "19     3     0.8806436211511175\n",
      "19     4     -1.7889286515241918\n",
      "19     5     -2.1968235535811216\n",
      "19     6     -0.2195586080694667\n",
      "19     7     1.9872618949914362\n",
      "19     8     2.9013931043038736\n",
      "19     9     2.5433180255656920\n",
      "19     10    1.6661531885921916\n",
      "19     11    0.8767269736906436\n",
      "19     12    0.3829113526754131\n",
      "19     13    0.1410214522949818\n",
      "19     14    0.0440452755504862\n",
      "19     15    0.0116375137667891\n",
      "19     16    0.0025711976543700\n",
      "19     17    0.0004631618670330\n",
      "19     18    0.0000644949195663\n",
      "19     19    0.0000060405026585\n",
      "\n",
      "20     0     -1.3894688729282854\n",
      "20     1     -1.1916029139984239\n",
      "20     2     1.7678021455184365\n",
      "20     3     1.7992868604931556\n",
      "20     4     -0.8550277976079781\n",
      "20     5     -2.4095712882443525\n",
      "20     6     -1.2474135108582378\n",
      "20     7     1.1139784909853621\n",
      "20     8     2.6870178558287119\n",
      "20     9     2.8524340980275609\n",
      "20     10    2.1361133458096004\n",
      "20     11    1.2597449298212475\n",
      "20     12    0.6123882033391261\n",
      "20     13    0.2509785767633770\n",
      "20     14    0.0876545312140856\n",
      "20     15    0.0261610714165858\n",
      "20     16    0.0066436792755485\n",
      "20     17    0.0014173229142183\n",
      "20     18    0.0002474378620958\n",
      "20     19    0.0000334962076255\n",
      "20     20    0.0000030577714179\n",
      "\n",
      "21     0     -0.8112645273811050\n",
      "21     1     -1.9906937070709074\n",
      "21     2     0.8282666860842647\n",
      "21     3     2.2681309539490946\n",
      "21     4     0.2773825216392514\n",
      "21     5     -2.1057471396768666\n",
      "21     6     -2.0353638835594494\n",
      "21     7     0.0713816500431441\n",
      "21     8     2.1560627200749685\n",
      "21     9     2.9527561864710177\n",
      "21     10    2.5653666544483080\n",
      "21     11    1.7011396460286878\n",
      "21     12    0.9188413375640805\n",
      "21     13    0.4169005312592605\n",
      "21     14    0.1614309544658579\n",
      "21     15    0.0537279667280125\n",
      "21     16    0.0153795469289819\n",
      "21     17    0.0037646659639955\n",
      "21     18    0.0007772402758153\n",
      "21     19    0.0001317495935741\n",
      "21     20    0.0000173648036246\n",
      "21     21    0.0000015469796608\n",
      "\n",
      "22     0     -0.0152845499763925\n",
      "22     1     -2.2591459584006133\n",
      "22     2     -0.3269353258959933\n",
      "22     3     2.1668673352012053\n",
      "22     4     1.3420810480049483\n",
      "22     5     -1.3410780755895670\n",
      "22     6     -2.4207659407000675\n",
      "22     7     -0.9774912507175768\n",
      "22     8     1.3407683164999220\n",
      "22     9     2.7789136762776478\n",
      "22     10    2.8783070270583684\n",
      "22     11    2.1622654900226403\n",
      "22     12    1.2987068159675277\n",
      "22     13    0.6505140822336841\n",
      "22     14    0.2776794290038595\n",
      "22     15    0.1021516325106981\n",
      "22     16    0.0325317625821935\n",
      "22     17    0.0089592775763944\n",
      "22     18    0.0021191380730175\n",
      "22     19    0.0004242502884869\n",
      "22     20    0.0000699393597606\n",
      "22     21    0.0000089871396946\n",
      "22     22    0.0000007822301059\n",
      "\n",
      "23     0     0.7848149987161793\n",
      "23     1     -1.9251715009787709\n",
      "23     2     -1.3962788532178152\n",
      "23     3     1.5182142444201188\n",
      "23     4     2.0829805803146262\n",
      "23     5     -0.2782332757671515\n",
      "23     6     -2.3137659528867109\n",
      "23     7     -1.8480053971253205\n",
      "23     8     0.3340857376252577\n",
      "23     9     2.3011417562288936\n",
      "23     10    2.9972314514043212\n",
      "23     11    2.5859257667592015\n",
      "23     12    1.7333850803673618\n",
      "23     13    0.9577888089363449\n",
      "23     14    0.4490933625030168\n",
      "23     15    0.1814952187422249\n",
      "23     16    0.0637231909607160\n",
      "23     17    0.0194853936302104\n",
      "23     18    0.0051769053358441\n",
      "23     19    0.0011857681598248\n",
      "23     20    0.0002306023108453\n",
      "23     21    0.0000370257190144\n",
      "23     22    0.0000046442339341\n",
      "23     23    0.0000003953434467\n",
      "\n",
      "24     0     1.3743292695760498\n",
      "24     1     -1.0776538252443455\n",
      "24     2     -2.0995004459740434\n",
      "24     3     0.4844562024975421\n",
      "24     4     2.3178090824031523\n",
      "24     5     0.8457794362576511\n",
      "24     6     -1.7244594469975221\n",
      "24     7     -2.3721474801887288\n",
      "24     8     -0.7197065733336340\n",
      "24     9     1.5398220861198548\n",
      "24     10    2.8580784799700667\n",
      "24     11    2.9017359816113264\n",
      "24     12    2.1866617887729873\n",
      "24     13    1.3346906159485556\n",
      "24     14    0.6862164261566049\n",
      "24     15    0.3034123552234957\n",
      "24     16    0.1166922546057132\n",
      "24     17    0.0392526963326761\n",
      "24     18    0.0115589072258463\n",
      "24     19    0.0029695842620829\n",
      "24     20    0.0006599303773460\n",
      "24     21    0.0001248668879319\n",
      "24     22    0.0000195523619810\n",
      "24     23    0.0000023966422763\n",
      "24     24    0.0000001997201897\n",
      "\n",
      "25     0     1.5951036348371481\n",
      "25     1     0.0574004673807631\n",
      "25     2     -2.2514844969503827\n",
      "25     3     -0.6722550049648113\n",
      "25     4     1.9854572080225155\n",
      "25     5     1.7725863369963142\n",
      "25     6     -0.7683790658312701\n",
      "25     7     -2.4376811322899705\n",
      "25     8     -1.6479570602875711\n",
      "25     9     0.5715885061410764\n",
      "25     10    2.4272805191322426\n",
      "25     11    3.0362989173253063\n",
      "25     12    2.6052123441242325\n",
      "25     13    1.7633158805316391\n",
      "25     14    0.9940334723502262\n",
      "25     15    0.4796730349837200\n",
      "25     16    0.2011768135648843\n",
      "25     17    0.0739479312439374\n",
      "25     18    0.0239091799747447\n",
      "25     19    0.0067976979943617\n",
      "25     20    0.0016922198673381\n",
      "25     21    0.0003654850745336\n",
      "25     22    0.0000673780459280\n",
      "25     23    0.0000103014903934\n",
      "25     24    0.0000012352011565\n",
      "25     25    0.0000001008537521\n",
      "\n",
      "26     0     1.3879396041147203\n",
      "26     1     1.1770806951197219\n",
      "26     2     -1.8115290337385765\n",
      "26     3     -1.6561890959165200\n",
      "26     4     1.1641529487093529\n",
      "26     5     2.2835615067671799\n",
      "26     6     0.3529858962955303\n",
      "26     7     -2.0186479917133076\n",
      "26     8     -2.2826870593795050\n",
      "26     9     -0.4762050575919476\n",
      "26     10    1.7158743085985901\n",
      "26     11    2.9271359762352822\n",
      "26     12    2.9231746107484478\n",
      "26     13    2.2095460324407297\n",
      "26     14    1.3681411566864490\n",
      "26     15    0.7197991784745474\n",
      "26     16    0.3282294014505007\n",
      "26     17    0.1312097411783896\n",
      "26     18    0.0462616978765384\n",
      "26     19    0.0144175153388032\n",
      "26     20    0.0039665404130688\n",
      "26     21    0.0009585575118592\n",
      "26     22    0.0002015121396241\n",
      "26     23    0.0000362413217334\n",
      "26     24    0.0000054160938570\n",
      "26     25    0.0000006358587128\n",
      "26     26    0.0000000509094409\n",
      "\n",
      "27     0     0.8084445850466733\n",
      "27     1     1.9824153371814115\n",
      "27     2     -0.8947367385213467\n",
      "27     3     -2.2140472282231487\n",
      "27     4     0.0547844658181353\n",
      "27     5     2.2540289526856934\n",
      "27     6     1.3937842096581072\n",
      "27     7     -1.1887441110692438\n",
      "27     8     -2.4971550250268750\n",
      "27     9     -1.4434829234297655\n",
      "27     10    0.7868312358979552\n",
      "27     11    2.5380554421741750\n",
      "27     12    3.0710330806679718\n",
      "27     13    2.6233971145671942\n",
      "27     14    1.7912643737677101\n",
      "27     15    1.0279430370223750\n",
      "27     16    0.5087972623055754\n",
      "27     17    0.2204558873759995\n",
      "27     18    0.0843365010215437\n",
      "27     19    0.0286100392851566\n",
      "27     20    0.0086154433101639\n",
      "27     21    0.0022981713708256\n",
      "27     22    0.0005400190490356\n",
      "27     23    0.0001106511639630\n",
      "27     24    0.0000194363965172\n",
      "27     25    0.0000028420285869\n",
      "27     26    0.0000003269718043\n",
      "27     27    0.0000000256893311\n",
      "\n",
      "28     0     0.0120875164815080\n",
      "28     1     2.2582500094189202\n",
      "28     2     0.2577500170779297\n",
      "28     3     -2.2009465050083272\n",
      "28     4     -1.0673941573664678\n",
      "28     5     1.6864859137244919\n",
      "28     6     2.1187730693490532\n",
      "28     7     -0.1125618368988448\n",
      "28     8     -2.2375715537392824\n",
      "28     9     -2.1657387339407772\n",
      "28     10    -0.2475813224936692\n",
      "28     11    1.8726751049049324\n",
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      "28     13    2.9429620909535990\n",
      "28     14    2.2311130600891449\n",
      "28     15    1.3994093145971649\n",
      "28     16    0.7515117290829660\n",
      "28     17    0.3521834995597979\n",
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      "28     19    0.0535066349345339\n",
      "28     20    0.0175112011841275\n",
      "28     21    0.0051061737877678\n",
      "28     22    0.0013229595712297\n",
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      "28     24    0.0000605309226236\n",
      "28     25    0.0000103956631082\n",
      "28     26    0.0000014886402668\n",
      "28     27    0.0000001679657974\n",
      "28     28    0.0000000129588426\n",
      "\n",
      "29     0     -0.7875202433444778\n",
      "29     1     1.9307985532993128\n",
      "29     2     1.3420260450634645\n",
      "29     3     -1.6189442610394900\n",
      "29     4     -1.9210913548677022\n",
      "29     5     0.7135063153754078\n",
      "29     6     2.3588941711378784\n",
      "29     7     0.9852068703650312\n",
      "29     8     -1.5417490613207434\n",
      "29     9     -2.5075258153568734\n",
      "29     10    -1.2397456811103977\n",
      "29     11    0.9824883503886497\n",
      "29     12    2.6361943020849172\n",
      "29     13    3.1022340261596315\n",
      "29     14    2.6406170870457411\n",
      "29     15    1.8174948130612376\n",
      "29     16    1.0598139686058841\n",
      "29     17    0.5366023578982321\n",
      "29     18    0.2393242065227578\n",
      "29     19    0.0948366688520069\n",
      "29     20    0.0335518431490483\n",
      "29     21    0.0106179496474806\n",
      "29     22    0.0030037468667707\n",
      "29     23    0.0007570810789999\n",
      "29     24    0.0001689099220078\n",
      "29     25    0.0000329983125977\n",
      "29     26    0.0000055462691029\n",
      "29     27    0.0000007784420199\n",
      "29     28    0.0000000862030938\n",
      "29     29    0.0000000065350397\n",
      "\n",
      "30     0     -1.3759232466698239\n",
      "30     1     1.0874519821836359\n",
      "30     2     2.0716042910990700\n",
      "30     3     -0.6176407940378912\n",
      "30     4     -2.2902122583661084\n",
      "30     5     -0.4316258091236482\n",
      "30     6     2.0537012349287549\n",
      "30     7     1.8669599285443770\n",
      "30     8     -0.5387572846616302\n",
      "30     9     -2.3940052515737391\n",
      "30     10    -2.0307461232963449\n",
      "30     11    -0.0336030596548713\n",
      "30     12    2.0132211592670739\n",
      "30     13    3.0422242528618209\n",
      "30     14    2.9613581172620238\n",
      "30     15    2.2515212265320033\n",
      "30     16    1.4287768719523375\n",
      "30     17    0.7815613007330453\n",
      "30     18    0.3753262534345103\n",
      "30     19    0.1599934103426492\n",
      "30     20    0.0609437329444411\n",
      "30     21    0.0208176003790814\n",
      "30     22    0.0063835212721452\n",
      "30     23    0.0017549244481434\n",
      "30     24    0.0004309020892594\n",
      "30     25    0.0000938514403547\n",
      "30     26    0.0000179312961425\n",
      "30     27    0.0000029521613343\n",
      "30     28    0.0000004064323328\n",
      "30     29    0.0000000442021891\n",
      "30     30    0.0000000032946366\n",
      "\n",
      "31     0     -1.5953317767669057\n",
      "31     1     -0.0464897280835923\n",
      "31     2     2.2532992638947480\n",
      "31     3     0.5437494920395682\n",
      "31     4     -2.0796780735677460\n",
      "31     5     -1.4702839249281059\n",
      "31     6     1.2694003900292530\n",
      "31     7     2.3355505122511571\n",
      "31     8     0.5722846116803634\n",
      "31     9     -1.8328960382762802\n",
      "31     10    -2.4806550746475846\n",
      "31     11    -1.0399341557854913\n",
      "31     12    1.1609208943802378\n",
      "31     13    2.7238135459754491\n",
      "31     14    3.1305105570789697\n",
      "31     15    2.6569840649654601\n",
      "31     16    1.8422209311917885\n",
      "31     17    1.0898888969571685\n",
      "31     18    0.5632066906316491\n",
      "31     19    0.2577812384582610\n",
      "31     20    0.1054067165871433\n",
      "31     21    0.0387027811404827\n",
      "31     22    0.0127929444179689\n",
      "31     23    0.0038079755502933\n",
      "31     24    0.0010188821679494\n",
      "31     25    0.0002440277884254\n",
      "31     26    0.0000519426866783\n",
      "31     27    0.0000097148783543\n",
      "31     28    0.0000015679767713\n",
      "31     29    0.0000002118951030\n",
      "31     30    0.0000000226468828\n",
      "31     31    0.0000000016605500\n",
      "\n",
      "32     0     -1.3869241071822034\n",
      "32     1     -1.1679779251878342\n",
      "32     2     1.8386419806138807\n",
      "32     3     1.5633187216276578\n",
      "32     4     -1.3411017859262540\n",
      "32     5     -2.1466841964316408\n",
      "32     6     0.1868276516902538\n",
      "32     7     2.2812941246849276\n",
      "32     8     1.5611918536135907\n",
      "32     9     -0.9205280523317589\n",
      "32     10    -2.4990523956368169\n",
      "32     11    -1.8844162961075728\n",
      "32     12    0.1663871683314349\n",
      "32     13    2.1399293633140744\n",
      "32     14    3.0908565867351649\n",
      "32     15    2.9785656299793990\n",
      "32     16    2.2709011049784529\n",
      "32     17    1.4564736394400499\n",
      "32     18    0.8101220018064087\n",
      "32     19    0.3977068077929490\n",
      "32     20    0.1741980229359608\n",
      "32     21    0.0685361544421763\n",
      "32     22    0.0243160382898109\n",
      "32     23    0.0077929105764669\n",
      "32     24    0.0022553881585085\n",
      "32     25    0.0005881310162647\n",
      "32     26    0.0001375585693017\n",
      "32     27    0.0000286436363698\n",
      "32     28    0.0000052487820963\n",
      "32     29    0.0000008311176031\n",
      "32     30    0.0000001103227549\n",
      "32     31    0.0000000115941595\n",
      "32     32    0.0000000008367364\n",
      "\n",
      "33     0     -0.8066038634727046\n",
      "33     1     -1.9772055423485104\n",
      "33     2     0.9370679428116753\n",
      "33     3     2.1750845903383800\n",
      "33     4     -0.2611335651766136\n",
      "33     5     -2.2919643578258739\n",
      "33     6     -0.9389892344936009\n",
      "33     7     1.7107933825962021\n",
      "33     8     2.2157314977725626\n",
      "33     9     0.1711945679578746\n",
      "33     10    -2.0688277409803586\n",
      "33     11    -2.4256886251614125\n",
      "33     12    -0.8459663999530576\n",
      "33     13    1.3241837886517565\n",
      "33     14    2.8025803549587658\n",
      "33     15    3.1563347021786248\n",
      "33     16    2.6725906024598300\n",
      "33     17    1.8656181541132526\n",
      "33     18    1.1183689918293629\n",
      "33     19    0.5887135574365213\n",
      "33     20    0.2758315384909388\n",
      "33     21    0.1160131971186337\n",
      "33     22    0.0440348979622273\n",
      "33     23    0.0151283973180420\n",
      "33     24    0.0047090740890291\n",
      "33     25    0.0013270498748069\n",
      "33     26    0.0003376746391437\n",
      "33     27    0.0000772092053725\n",
      "33     28    0.0000157420728970\n",
      "33     29    0.0000028284982986\n",
      "33     30    0.0000004397091079\n",
      "33     31    0.0000000573664205\n",
      "33     32    0.0000000059313928\n",
      "33     33    0.0000000004215257\n",
      "\n",
      "34     0     -0.0099944606454569\n",
      "34     1     -2.2577775769375314\n",
      "34     2     -0.2127689899759924\n",
      "34     3     2.2187478159202292\n",
      "34     4     0.8851212585971365\n",
      "34     5     -1.8677614987881230\n",
      "34     6     -1.8387739286685576\n",
      "34     7     0.7495234796999792\n",
      "34     8     2.3898081583737509\n",
      "34     9     1.2258507097506959\n",
      "34     10    -1.2569584148427166\n",
      "34     11    -2.5620996168217212\n",
      "34     12    -1.7315273913026852\n",
      "34     13    0.3532464360246812\n",
      "34     14    2.2547669226651905\n",
      "34     15    3.1348126223759110\n",
      "34     16    2.9947460506539523\n",
      "34     17    2.2893617191802589\n",
      "34     18    1.4826895684371424\n",
      "34     19    0.8373415676099812\n",
      "34     20    0.4193713301967082\n",
      "34     21    0.1882504953149449\n",
      "34     22    0.0762528213999838\n",
      "34     23    0.0279875503556861\n",
      "34     24    0.0093282640327297\n",
      "34     25    0.0028245975767508\n",
      "34     26    0.0007760847389880\n",
      "34     27    0.0001929149300563\n",
      "34     28    0.0000431632028742\n",
      "34     29    0.0000086243100455\n",
      "34     30    0.0000015205557276\n",
      "34     31    0.0000002322202112\n",
      "34     32    0.0000000297942508\n",
      "34     33    0.0000000030323496\n",
      "34     34    0.0000000002123069\n",
      "\n",
      "35     0     0.7892996301573407\n",
      "35     1     -1.9346140108581913\n",
      "35     2     -1.3060742156776253\n",
      "35     3     1.6821683508463563\n",
      "35     4     1.8040605860716730\n",
      "35     5     -0.9776962513088576\n",
      "35     6     -2.2942290823017046\n",
      "35     7     -0.3838274464174742\n",
      "35     8     2.0392965422580218\n",
      "35     9     2.0260596116567227\n",
      "35     10    -0.2082402683092734\n",
      "35     11    -2.2563206466848360\n",
      "35     12    -2.3496775846780711\n",
      "35     13    -0.6589358575046262\n",
      "35     14    1.4740539636305674\n",
      "35     15    2.8738258256536824\n",
      "35     16    3.1800785024480387\n",
      "35     17    2.6875142789290081\n",
      "35     18    1.8878323170232800\n",
      "35     19    1.1454229615396720\n",
      "35     20    0.6132135519480584\n",
      "35     21    0.2934829839051948\n",
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      "35     23    0.0495236404726502\n",
      "35     24    0.0176127188899557\n",
      "35     25    0.0057046683684478\n",
      "35     26    0.0016827084021061\n",
      "35     27    0.0004513152728081\n",
      "35     28    0.0001097051916470\n",
      "35     29    0.0000240402100686\n",
      "35     30    0.0000047109064558\n",
      "35     31    0.0000008155747366\n",
      "35     32    0.0000001224370592\n",
      "35     33    0.0000000154568097\n",
      "35     34    0.0000000015492589\n",
      "35     35    0.0000000001069090\n",
      "\n",
      "36     0     1.3769697136760397\n",
      "36     1     -1.0940802673128878\n",
      "36     2     -2.0527164047286712\n",
      "36     3     0.7051781711821197\n",
      "36     4     2.2590846813549046\n",
      "36     5     0.1568790341547655\n",
      "36     6     -2.1924391813409270\n",
      "36     7     -1.4263526849174579\n",
      "36     8     1.2361777399810796\n",
      "36     9     2.4004890809783657\n",
      "36     10    0.8784935080304761\n",
      "36     11    -1.5495035800315837\n",
      "36     12    -2.5909637287977310\n",
      "36     13    -1.5754873400233518\n",
      "36     14    0.5279047177437799\n",
      "36     15    2.3593491745868325\n",
      "36     16    3.1747979214452751\n",
      "36     17    3.0100297804683560\n",
      "36     18    2.3069951061455534\n",
      "36     19    1.5075835182420145\n",
      "36     20    0.8633464645684568\n",
      "36     21    0.4403628402853830\n",
      "36     22    0.2021376019517379\n",
      "36     23    0.0840674463849875\n",
      "36     24    0.0318148276300025\n",
      "36     25    0.0109833162424559\n",
      "36     26    0.0034622484209411\n",
      "36     27    0.0009961178918871\n",
      "36     28    0.0002610792282578\n",
      "36     29    0.0000621180697092\n",
      "36     30    0.0000133428393735\n",
      "36     31    0.0000025661548317\n",
      "36     32    0.0000004365159507\n",
      "36     33    0.0000000644535266\n",
      "36     34    0.0000000080102836\n",
      "36     35    0.0000000007910545\n",
      "36     36    0.0000000000538244\n",
      "\n",
      "37     0     1.5954600375003904\n",
      "37     1     0.0390621305411796\n",
      "37     2     -2.2543164224998242\n",
      "37     3     -0.4565361848218690\n",
      "37     4     2.1320889773596261\n",
      "37     5     1.2514019052273915\n",
      "37     6     -1.5555057716236789\n",
      "37     7     -2.1322940936716002\n",
      "37     8     0.1563082484796161\n",
      "37     9     2.2636433232964190\n",
      "37     10    1.7880455475968271\n",
      "37     11    -0.5604952058340800\n",
      "37     12    -2.4017887951884478\n",
      "37     13    -2.2580649915096953\n",
      "37     14    -0.4793988098329115\n",
      "37     15    1.6120645364687798\n",
      "37     16    2.9386256150235717\n",
      "37     17    3.2020394711542566\n",
      "37     18    2.7018208351381845\n",
      "37     19    1.9089860231980720\n",
      "37     20    1.1711937262404053\n",
      "37     21    0.6367865135866430\n",
      "37     22    0.3107455687025373\n",
      "37     23    0.1372330965707148\n",
      "37     24    0.0551474383313888\n",
      "37     25    0.0202348757868065\n",
      "37     26    0.0067919663796626\n",
      "37     27    0.0020865528972440\n",
      "37     28    0.0005862151128435\n",
      "37     29    0.0001502936618361\n",
      "37     30    0.0000350316232460\n",
      "37     31    0.0000073814050848\n",
      "37     32    0.0000013942243958\n",
      "37     33    0.0000002331664221\n",
      "37     34    0.0000000338797606\n",
      "37     35    0.0000000041470780\n",
      "37     36    0.0000000004036833\n",
      "37     37    0.0000000000270934\n",
      "\n",
      "38     0     1.3862023754765427\n",
      "38     1     1.1617398627833144\n",
      "38     2     -1.8571014324840638\n",
      "38     3     -1.4982113650024236\n",
      "38     4     1.4547938333794090\n",
      "38     5     2.0295084613106735\n",
      "38     6     -0.5372910121620587\n",
      "38     7     -2.3322336096362783\n",
      "38     8     -0.9576956068989364\n",
      "38     9     1.6386255450233902\n",
      "38     10    2.3331507767883712\n",
      "38     11    0.5314825029085819\n",
      "38     12    -1.8008896479539835\n",
      "38     13    -2.5921007747435150\n",
      "38     14    -1.4187234406883980\n",
      "38     15    0.6912944601511337\n",
      "38     16    2.4550136194183909\n",
      "38     17    3.2113807274186956\n",
      "38     18    3.0245236100403674\n",
      "38     19    2.3238797217647713\n",
      "38     20    1.5312897308928262\n",
      "38     21    0.8882458128158834\n",
      "38     22    0.4607212330648123\n",
      "38     23    0.2158502493620957\n",
      "38     24    0.0919577376255383\n",
      "38     25    0.0357821225987181\n",
      "38     26    0.0127517685598488\n",
      "38     27    0.0041676006393171\n",
      "38     28    0.0012492869977603\n",
      "38     29    0.0003431011778331\n",
      "38     30    0.0000861240296073\n",
      "38     31    0.0000196817883098\n",
      "38     32    0.0000040709634533\n",
      "38     33    0.0000007556498885\n",
      "38     34    0.0000001243115087\n",
      "38     35    0.0000000177840024\n",
      "38     36    0.0000000021449952\n",
      "38     37    0.0000000002058924\n",
      "38     38    0.0000000000136356\n",
      "\n",
      "39     0     0.8053085866551439\n",
      "39     1     1.9736272187970763\n",
      "39     2     -0.9663994527158715\n",
      "39     3     -2.1460102640394179\n",
      "39     4     0.4014335039998116\n",
      "39     5     2.2933208306700381\n",
      "39     6     0.6127562908929870\n",
      "39     7     -1.9754834190632793\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "46     46    0.0000000000000558\n",
      "\n",
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      "47     47    0.0000000000000281\n",
      "\n",
      "48     0     1.3782581202098443\n",
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      "48     22    3.3569333306921831\n",
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      "48     24    2.3991477565413613\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "54     54    0.0000000000000002\n",
      "\n",
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      "55     55    0.0000000000000001\n",
      "\n",
      "56     0     -1.3849136223535541\n",
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      "56     2     1.8885811661639824\n",
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    }
   ],
   "source": [
    "import decimal\n",
    "from math import *\n",
    "import numpy as np\n",
    "from torch import short\n",
    "\n",
    "# 定义初始值\n",
    "l = 181\n",
    "theta = 30 * pi / 180\n",
    "\n",
    "# 初始化dp，创建181x181的矩阵\n",
    "dp = np.zeros((l, l))\n",
    "\n",
    "# 定义种子点\n",
    "dp[0][0] = 1\n",
    "dp[1][0] = sqrt(3) * cos(theta)\n",
    "dp[1][1] = sqrt(3) * sin(theta)\n",
    "\n",
    "# 求出坐标为[i,i],[i,i-1]的点\n",
    "for i in range(2, l):\n",
    "    f1 = sqrt((2 * i + 1) / (2 * i))\n",
    "    f2 = sqrt(2 * i + 1)\n",
    "    dp[i][i] = f1 * sin(theta) * dp[i - 1][i - 1]\n",
    "    dp[i][i - 1] = f2 * cos(theta) * dp[i - 1][i - 1]\n",
    "\n",
    "# 使用前面的结果递推出坐标为[row,lie]的点\n",
    "for lie in range(0, l):\n",
    "    for row in range(lie + 2, l):\n",
    "        f3 = sqrt((2 * row + 1) / ((row - lie) * (row + lie)))\n",
    "        f4 = sqrt(2 * row - 1)\n",
    "        f5 = sqrt(((row - lie - 1) * (row + lie - 1)) / (2 * row - 3))\n",
    "        dp[row][lie] = (\n",
    "            f3 * f4 * cos(theta) * dp[row - 1][lie] - f3 * f5 * dp[row - 2][lie]\n",
    "        )\n",
    "\n",
    "# 将矩阵多余值设为空\n",
    "for i in range(0, l):\n",
    "    for j in range(i, l - 1):\n",
    "        dp[i][j + 1] = None\n",
    "\n",
    "# 创建结果展示列表show_p\n",
    "show_p = list()\n",
    "\n",
    "# 标题设置\"{:<7s}{:<6s}{:.16s}\\n\"为占位符，分别表示\"L\",\"M\",\"P_l_m\"\n",
    "show_p.append(\n",
    "    \"学号：2022302141211\\n姓名：刘维康\\n标准向前列递推法\\n-----------------------\\n\"\n",
    ")\n",
    "show_p.append(\"{:<7s}{:<6s}{:.16s}\\n\".format(\"L\", \"M\", \"P_l_m\"))\n",
    "\n",
    "# 对show_p列表进行填充\n",
    "for i in range(0, l):\n",
    "    for j in range(0, i + 1):\n",
    "        line = \"{:<7d}{:<6d}{:.16f}\\n\".format(int(i), int(j), dp[i][j])\n",
    "        show_p.append(line)\n",
    "    show_p.append(\"\\n\")\n",
    "\n",
    "# print文件数据\n",
    "print(\"\".join(show_p))\n",
    "\n",
    "# 输出结果到文件2022302141211_leiderang.txt\n",
    "with open(\"2022302141211_刘维康.txt\", \"w\") as f:\n",
    "    f.writelines(show_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from decimal import *\n",
    "\n",
    "# getcontext().prec = 21\n",
    "# print(Decimal(1.1) / Decimal(1))"
   ]
  }
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